This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.
Submitted August 31, 2009. Published July 7, 2010.
Math Subject Classifications: 35Q30.
Key Words: Partial differential equations; Navier-Stokes equation; fluid dynamics.
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| Jorma Jormakka |
National Defence University
P.O. Box 07 00861 Helsinki, Finland
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